Finite groups of units of finite characteristic rings

In \cite[Problem 72]{Fuchs60} Fuchs asked the following question: which groups can be the group of units of a commutative ring? In the following years, some partial answers have been given to this question in particular cases. The aim of the present paper is to address Fuchs' question when $A$ is a {\it finite characteristic ring}. The result is a pretty good description of the groups which can occur as group of units in this case, equipped with examples showing that there are obstacles to a "short" complete classification. As a byproduct, we are able to classify all possible cardinalities of the group of units of a finite characteristic ring, so to answer Ditor's question \cite{ditor}

On wild extensions of a p-adic field

In this paper we consider the problem of classifying the isomorphism classes of extensions of degree pk of a p-adic field, restricting to the case of extensions without intermediate fields. We establish a correspondence between the isomorphism classes of these extensions and some Kummer extensions of a suitable field F containing K. We then describe such classes in terms of the representations of Gal(F/K). Finally, for k = 2 and for each possible Galois group G, we count the number of isomorphism classes of the extensions whose normal closure has a Galois group isomorphic to G. As a byproduct, we get the total number of isomorphism classes

Separatrix Reconnections in Chaotic Regimes

In this paper we extend the concept of separatrix reconnection into chaotic regimes. We show that even under chaotic conditions one can still understand abrupt jumps of diffusive-like processes in the relevant phase-space in terms of relatively smooth realignments of stable and unstable manifolds of unstable fixed points.Comment: 4 pages, 5 figures, submitted do Phys. Rev. E (1998

A QR based approach for the nonlinear eigenvalue problem

We describe a fast and numerically robust approach based on the structured QR eigenvalue algorithm for computing approximations of the eigenvalues of a holomorphic matrix-valued function inside the unit circle. Numerical experiments confirm the effectiveness of the proposed method

Gershgorin disks for multiple eigenvalues of non-negative matrices

Gershgorin's famous circle theorem states that all eigenvalues of a square matrix lie in disks (called Gershgorin disks) around the diagonal elements. Here we show that if the matrix entries are non-negative and an eigenvalue has geometric multiplicity at least two, then this eigenvalue lies in a smaller disk. The proof uses geometric rearrangement inequalities on sums of higher dimensional real vectors which is another new result of this paper

In Search of Differential Inhibitors of Aldose Reductase

Aldose reductase, classified within the aldo-keto reductase family as AKR1B1, is an NADPH dependent enzyme that catalyzes the reduction of hydrophilic as well as hydrophobic aldehydes. AKR1B1 is the first enzyme of the so-called polyol pathway that allows the conversion of glucose into sorbitol, which in turn is oxidized to fructose by sorbitol dehydrogenase. The activation of the polyol pathway in hyperglycemic conditions is generally accepted as the event that is responsible for a series of long-term complications of diabetes such as retinopathy, cataract, nephropathy and neuropathy. The role of AKR1B1 in the onset of diabetic complications has made this enzyme the target for the development of molecules capable of inhibiting its activity. Virtually all synthesized compounds have so far failed as drugs for the treatment of diabetic complications. This failure may be partly due to the ability of AKR1B1 to reduce alkenals and alkanals, produced in oxidative stress conditions, thus acting as a detoxifying agent. In recent years we have proposed an alternative approach to the inhibition of AKR1B1, suggesting the possibility of a differential inhibition of the enzyme through molecules able to preferentially inhibit the reduction of either hydrophilic or hydrophobic substrates. The rationale and examples of this new generation of aldose reductase differential inhibitors (ARDIs) are presented

Pathways of 4-hydroxy-2-nonenal detoxification in a human astrocytoma cell line

One of the consequences of the increased level of oxidative stress that often characterizes the cancer cell environment is the abnormal generation of lipid peroxidation products, above all 4-hydroxynonenal. The contribution of this aldehyde to the pathogenesis of several diseases is well known. In this study, we characterized the ADF astrocytoma cell line both in terms of its pattern of enzymatic activities devoted to 4-hydroxynonenal removal and its resistance to oxidative stress induced by exposure to hydrogen peroxide. A comparison with lens cell lines, which, due to the ocular function, are normally exposed to oxidative conditions is reported. Our results show that, overall, ADF cells counteract oxidative stress conditions better than normal cells, thus confirming the redox adaptation demonstrated for several cancer cells. In addition, the markedly high level of NADP+-dependent dehydrogenase activity acting on the glutahionyl-hydroxynonanal adduct detected in ADF cells may promote, at the same time, the detoxification and recovery of cell-reducing power in these cells

Rupture Of Abdominal Aortic Aneurysm Due To Endograft Infection After Endovascular Aneurysm Repair (EVAR): A Case Report

Endograft infection is a rare event, with few reports in the literature. This report describes delayed infection of an aortic endoprosthesis that eventually resulted in abdominal aortic aneurysm (AAA) rupture. The procedure was performed in an angiographic suite. In the postoperative period the patient developed a central venous line infection. This appears to be the first recognized and reported case in which the infected aortic neck completely dilated due to the radial force of the stent graft

L-Idose: an attractive substrate alternative to d-glucose for measuring aldose reductase activity

Although glucose is one of the most important physio-pathological substrates of aldose reductase, it is not an easy molecule for in vitro investigation into the enzyme. In many cases alternative aldoses have been used for kinetic characterization and inhibition studies. However these molecules do not completely match the structural features of glucose, thus possibly leading to results that are not fully applicable to glucose. We show how aldose reductase is able to act efficiently on L-idose, the C-5 epimer of D-glucose. This is verified using both the bovine lens and the human recombinant enzymes. While the kcat values obtained are essentially identical to those measured for D-glucose, a significant decrease in KM was observed. This can be due to the significantly higher level of the free aldehyde form present in L-idose compared to D-glucose. We believe that L-idose is the best alternative to D-glucose in studies on aldose reductase

In search for multi-target ligands as potential agents for diabetes mellitus and its complications—a structure-activity relationship study on inhibitors of aldose reductase and protein tyrosine phosphatase 1b

Diabetes mellitus (DM) is a complex disease which currently affects more than 460 million people and is one of the leading cause of death worldwide. Its development implies numerous metabolic dysfunctions and the onset of hyperglycaemia-induced chronic complications. Multiple ligands can be rationally designed for the treatment of multifactorial diseases, such as DM, with the precise aim of simultaneously controlling multiple pathogenic mechanisms related to the disease and providing a more effective and safer therapeutic treatment compared to combinations of selective drugs. Starting from our previous findings that highlighted the possibility to target both aldose reductase (AR) and protein tyrosine phosphatase 1B (PTP1B), two enzymes strictly implicated in the development of DM and its complications, we synthesised 3-(5-arylidene-4-oxothiazolidin-3-yl)propanoic acids and analogous 2-butenoic acid derivatives, with the aim of balancing the effectiveness of dual AR/PTP1B inhibitors which we had identified as designed multiple ligands (DMLs). Out of the tested compounds, 4f exhibited well-balanced AR/PTP1B inhibitory effects at low micromolar concentrations, along with interesting insulin-sensitizing activity in murine C2C12 cell cultures. The SARs here highlighted along with their rationalization by in silico docking experiments into both target enzymes provide further insights into this class of inhibitors for their development as potential DML antidiabetic candidates